Question: A group of adults and kids went to see a movie. Tickets cost $$7.50$ each for adults and $$4.50$ each for kids, and the group paid $$58.50$ in total. There were $5$ fewer adults than kids in the group. Find the number of adults and kids in the group.
Answer: Let $x$ equal the number of adults and $y$ equal the number of kids. The system of equations is then: ${7.5x+4.5y = 58.5}$ ${x = y-5}$ Solve for $x$ and $y$ using substitution. Since $x$ has already been solved for, substitute ${y-5}$ for $x$ in the first equation. ${7.5}{(y-5)}{+ 4.5y = 58.5}$ Simplify and solve for $y$ $ 7.5y-37.5 + 4.5y = 58.5 $ $ 12y-37.5 = 58.5 $ $ 12y = 96 $ $ y = \dfrac{96}{12} $ ${y = 8}$ Now that you know ${y = 8}$ , plug it back into ${x = y-5}$ to find $x$ ${x = }{(8)}{ - 5}$ ${x = 3}$ You can also plug ${y = 8}$ into ${7.5x+4.5y = 58.5}$ and get the same answer for $x$ ${7.5x + 4.5}{(8)}{= 58.5}$ ${x = 3}$ There were $3$ adults and $8$ kids.